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  "body": "\n## Summary\n\nA maximal torus of a compact Lie group is a subgroup isomorphic to a torus $\\mathbb{T}^k$ that is not contained in any larger such subgroup.\nIn a compact connected Lie group all maximal tori are conjugate, and every element lies in one of them.\nMuch of the theory of compact Lie groups is read off from a maximal torus and the action of the Weyl group on it.\n\n## Explanations\n\n### L1 human\n\nA torus inside a group is a family of commuting rotations, like several independent clock hands.\nA maximal torus is as large as such a family can be.\nIn the group $U(n)$ of unitary matrices, the diagonal matrices with entries on the unit circle form a maximal torus: there are $n$ independent angles.\nEvery unitary matrix can be diagonalised by a unitary change of basis, so every element of $U(n)$ lies in a conjugate of this torus.\n",
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